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Highlights from
Tutorial on solving DDEs with DDE23

  • exam1
  • exam1
  • exam2
  • exam2
  • exam3
  • exam3
  • exam4
  • exam4
  • exam5
  • exam5
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer5
  • exer5
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
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Tutorial on solving DDEs with DDE23

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22 Aug 2003 (Updated )

Solving delay differential equations with DDE23. Tutorial + Examples.

exam2
function sol = exam2
% Example 5 of D.R. Wille' and C.T.H. Baker, DELSOL--
% a numerical code for the solution of systems of delay-
% differential equations, Appl. Numer. Math., 9 (1992) 
% 223-234.  This is an example of a scalar equation that 
% exhibits chaotic behavior. Equation (7) of the paper 
% includes a parameter gamma, but no value is specified in
% the example.  A value of -1 gives qualitative agreement 
% with Fig. 3 of the paper.  The length of the interval of 
% integration is also not given.  Here an interval [0, 100] 
% is used; it is clearly shorter than that of the figure, 
% but the qualitative behavior is seen already.

% Copyright 2002, The MathWorks, Inc.

sol = dde23(@exam2f,2,0.5,[0, 100]);
t = linspace(2,100,1000);
y = deval(sol,t);
ylag = deval(sol,t - 2);
figure
plot(y,ylag)
title('Example 5 of Wille'' and Baker.')
xlabel('y(t)');
ylabel('y(t-2)');
axis([0 1.5 0 1.5])

%-----------------------------------------------------------------------

function yp = exam2f(t,y,Z)
%EXAM2F  The derivative function for the Example 2 of the DDE Tutorial.
yp = 2*Z/(1 + Z^9.65) - y;

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